From ba45d5d1e2146cf5af1407823fa9aba509783f30 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Tue, 4 Sep 2018 11:05:22 +1000 Subject: [PATCH] light-matter cheatsheet --- physics/light-matter-ref.md | 88 ++++++++++++++++++++++++++++++++++- physics/light-matter-ref.pdf | Bin 0 -> 178880 bytes 2 files changed, 87 insertions(+), 1 deletion(-) create mode 100644 physics/light-matter-ref.pdf diff --git a/physics/light-matter-ref.md b/physics/light-matter-ref.md index 386c83c..170d6a4 100644 --- a/physics/light-matter-ref.md +++ b/physics/light-matter-ref.md @@ -6,10 +6,96 @@ author: Andrew Lorimer --- \pagenumbering{gobble} +\usepackage{multicols} # Light and Matter +## Planck's equation + +$$f={c \over \lambda}$$ + $$E=hf={hc \over \lambda}$$ -$$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$ +$$h=6.63 \times 10^{-34}\operatorname{J s}=4.12 \times 10^{-15} \operatorname{eV s}$$ + +## Force of electrons + +$$F=evB$$ + +## Photoelectric effect + +- $V_{\operatorname{supply}}$ does not affect photocurrent +- if $V_{\operatorname{supply}} > 0$, e- are attracted to collector anode +- if $V_{\operatorname{supply}} < 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$ +- $v$ of e- depends on ionisation energy (shell) + +### Threshold frequency +- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected +- $x$-intercept of frequency vs $E_K$ graph +- if $f < f_0$, no photoelectrons are detected + +### Work function +- *work function* $\phi$ - minimum energy required to release photoelectrons +- magnitude of $y$-intercept of frequency vs $E_K$ graph +- $\phi$ is determined by strength of bonding + +$$\phi=hf_0$$ + +### Kinetic energy + +$$E_{\operatorname{k-max}}=hf - \phi$$ + +voltage in circuit = max $E_K$ in eV + +### Stopping potential + +_Smallest voltage to achieve minimum current_ + +$$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$ + +## De Broglie's theory + +$$\lambda = {h \over \rho} = {h \over mv}$$ +$$\rho = {hf \over c} = {h \over \lambda}$$ +$$E = \rho c$$ + +- impossible to confirm de Broglie's theory of matter with double-slit experiment, since wavelengths are much smaller than for light, requiring an equally small slit ($< r_{\operatorname{proton}}$) +- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit) +- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern + +## X-ray and electron interaction + +- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ +- rearranging this, $2\pi r = n{h \over mv}$ (circumference) +- if $2\pi r \ne n{h \over mv}$, interference occurs, standing wave cannot be established + +## Spectral analysis + + +- $\Delta E = hf = {hc \over \lambda}$ between ground / excited state +- $f$ of a photon emitted or absorbed can be calculated from energy difference: $E_2 – E_1 = hf$ or $= hc$ +- Ionisation energy - min $E$ required to remove e- +- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) + +## Indeterminancy principle + +measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. $\therefore, \sigma E \propto {1 \over \sigma t}$ + +$$\sigma E \sigma t \ge {h \over 4 \pi}$$ + +## Wave-particle duality +wave model: + +- cannot explain photoelectric effect +- $f$ is irrelevant to photocurrent +- predicts delay between incidence and ejection +- speed depends on medium + +particle model: +- explains photoelectric effect +- rate of photoelectron release $\propto$ intensity +- no time delay - one photon releases one electron +- double slit: photons interact as they pass through slits. interference pattern still appears when a dim light source is used so that only one photon can pass at a time +- light exerts force +- light bent by gravity \ No newline at end of file diff --git a/physics/light-matter-ref.pdf b/physics/light-matter-ref.pdf new file mode 100644 index 0000000000000000000000000000000000000000..70dc0a68f9f44e242cfe568809ee9e966ca10d25 GIT binary patch literal 178880 zcma&NLzpm1u(a8>ZQHhO+qUiQuWj45ZQHhOoBtWy)m_ZgrZVfPeN?=WMXDeoM$1UY z3Pn1ywr1sp$SF1IIxD3B*JRQG^v1O136=e8MH?bNGN2sq0Q0jm_H-jJCA{=x8> zfjAyM@k!x}14g4q6M_tqjS01DF=P2bLM1$EN>GdleJD^uf5r+3j+iKJwVI!PwVs>9 z5|C2xPS6sR#xRzYKhkxlp=Dd0^|=|X?EeZ@TP?0^SBCF{aaNWUQSMI#<(I_>pHEtB z><^BZd=Xo6p`u~Tl&|(`TW`?xhz9l>Ax`y;NB2Y5hKUoNN2?G(xkRqQ1##6uuXe=` zk0lTT1@c#g5Hf%4+Irs#_ctI|&uRJzi5EaM*1SnG_x!7XRH;=0Y1R|8ffrxt|6K z1^wGPx|0=HMq=a@c_B+Y!1ZjB}_aSD2pAbWBUtWCil^ZAMyV|#}a)!7c??rqlW z#D-|PGbUK^DB$zw|2QM0^WUT!BK8#7E-#l~?9brojN%|S=)@IEsD4(lEBLtu`uN%g z((gYcY~RV*BI6qS>_C(!v#LJ`;F94FlvnUaHf9JkD91eNt$x~}ij-K3=#$NI+_eUD zS%r0NAStvv%y=}(-fU+v4)s}e-9x3J`4e_%pUHKT> zmcS_G3p?CaA2FQzGPioFTDz5UD)bF3H<7p>s-83f!9TYRgS}9Rh`E>~HP*y;|A#d{ zh3#E=ovHC_vF@-_`E>leaXeLN^9IeGEH&)Dj^A*;*B+NjaPnM;RIU3>Pb27T2pJhA zrNE;UxI8gf`|y0~CdrjtfT9Ds9FO8V&(B#7gdz(abl#{NLwF_Ws!cm-g~>c3V9dUg zSk=PEcK+@G+$63J{<4o@AcJ~K11LfSYpyl9jH`*Uj{+v`>u>c0_HEbYD+KS$%`}A& z%D`WFoQ9~a0~H=Ynb#!ihpsJFAnU|yb~q(3SjtTeoQd}UFsk^9ds9uG2&{nwbP7valU9H;#qfk;s(U@9AUy}%^qhesf#f2j3h^1%dH}R?^e* zD?iqY`vlc@?nJBHkOQ}IKDqN;MBd|!Sx8!FeEU@tMPN*>-`g55{;i!|Ul|7x2qmF~%Ns%j2x+7! zC2F`M-VSczp4%SkS9*!jTY)uxRpYy~eIMLd;Z5#a-`ggSz8iA&iL~{PJGnZ9mR-8M#|2BdLa&TO^RDz6VGDQRj zM9vy}-%o52@b|lMupk&FFXkc_62-~AJnE0nQ(YFk)=$ZC|34BYsbZmEuLVrl@LGg1 zfpC%|>_cdh1}{+`F_c23UQwUHcq477=x#Hp<-C^+#c9Ux;vJ!Z%dE~43B->|?ef(r zN`D`S4$;Ekz}E<&^d#9H2$7vst#l$VB2uA&0l9Y`f{xhZVC=Sf+XqiBbpCzRae$I{ z?P759AV#+0x9Zcyujp_iu!>O$lpts23!hiUVr(#C(k#0HiTDH|?zN5ZCQMZsPGJmk z2O^HmtqWw*btK?0OzHgNSrVjf6jGHzVuYs9w8_urxQgu--#+rL$KJ)1z=oaqOZm>J zEwJK!U0Zy7s4ova36>T*lKbDLpH05?IWFwb!X|s3l%a(OfWcQ7@)2KExL3^w(Wr#m z$lB^CGk74_yK8#ijpN(-GF}Cf&#}2rc}3KjBL^2ElboVT))me*6fz2;Mul7w1egld z-nypBMj$KP#?jxm`Al&i^^~}=4jSEuv5xD>(*@j%^8?Cz&(=GPT)Ah(9(j#@g^ZB? z1;C^2A9h=yjw_wx^UY!#$Zxj%=pkB$mvC!3PoyF(f&K%o
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